In Denmark, the educational system has historically used a number of different systems of grading student performances, several of which are described below. The current grading system is the 7-trins-skala (7-step-scale) which replaced the 13-skala in 2006.

Furthermore, Undervisningsministeriet (the Ministry of Education) will adapt to a more international way of grading, by handing out a set number of grades per class. This is because in other countries, the grade A (12) is given twice as often as it is in Denmark (because of strict grading on absolute standards).

0 was an outright failing grade - there was a limitation of the number of non contemendus there could be in a passing student's examination. The highest grade, laudabilis præ ceteris was explicitly named a grade for exceptional purposes only.

The 13-scale was introduced in 1963 and used until 2006 (2007 in universities). The scale started out as a relative scale but has since its introduction in 1963 changed to an absolute scale at all levels of education.

13 - given for exceptionally independent and excellent performance.

11 - given for independent and excellent performance

10 - given for excellent but not particularly independent performance

9 - given for good performance, a little above average

8 - given for average performance

7 - given for mediocre performance, slightly below average

6 - given for just acceptable performance

5 - given for hesitant and not satisfactory performance

03 - given for very hesitant, very insufficient and unsatisfactory performance

00 - given for completely unacceptable performance

The gaps between 00 & 03, 03 & 5 and 11 & 13 are there to signify a larger difference between those grades. The leading 0 in 00 and 03 is used to prevent fraud with grades. The lowest passing grade is 6 and 00, 03 and 5 are failing grades.

The highest grade 13 and the lowest grade 00 are the grades most rarely given.

00 is nearly impossible to achieve, presuming one knows even a single fact taught in that particular class. It is given for a truly incompetent performance. At exams, 00 is given to students attending, but who cannot answer a single question. Absentees get a "-" and aren't allowed to attend a second exam.

13 is a fairly rare grade outside of exams and requires a performance way beyond the expected. One of the reasons why the 13 scale was replaced with the 7 scale was because of the grade 13. 13s are only given to the students that have gone above and beyond the stated curriculum. To gain it you needed to know more than what was taught in class. It required truly independent study. As no other EU countries used grades above perfect understanding of the curriculum, 13 was untranslatable to other grading systems.

In the table below, the Danish grading scale is compared with the ECTS and the U.S. academic grading scales (4.0/4.3/4.5) by World Education Services.